This invention relates in general to positional calibration methods and more particularly to calibration methods for use in correcting distorted measurements of position during production of integrated circuits. In contemporary photolithographic processing of wafers to generate integrated circuits, a succession of masks are utilized to control which areas of a wafer are etched, doped or coated during various processing steps. To ensure that features produced in one step using a first mask are accurately aligned with features produced in another step using a second mask, it is important that the two masks are accurately aligned with each other and that the features within each mask are accurately located within each mask.
The wafer is typically mounted on a wafer stage that can be translated in the two dimensional plane of the wafer. To accurately control such translations, many systems utilize an interferometer to measure the x-position and the y-position of the wafer stage. Even such an extremely accurate method of measuring position is becoming insufficiently accurate in contemporary processes in which sub-micron linewidths are being produced and in which alignment accuracies on the order of one-tenth of a micron are required. On this scale of accuracy, it is found that positions measured by the interferometers have small errors that can affect the quality of the circuits produced.
Such errors are significant in electron beam lithography because of the extremely small linewidths that can be produced. It is important in an electron beam system not only to accurately know the position of the wafer stage, but also to accurately know the position of the electron beam. Therefore, an electron beam system requires calibration of both the wafer stage translation apparatus and the electron beam deflectors.
Traditionally, positional calibration is effected by use of a calibration plate on which a Cartesian grid of points has been generated. To calibrate the interferometer measurements of the position of the wafer stage in an electron beam lithography system, the electron beam is utilized in a scanning electron microscope mode. In this mode, the electron beam deflectors are turned off so that the electron beam is undeflected. The calibration plate is mounted on the wafer stage and the wafer stage is translated to successively bring each of the grid points under the electron beam. The grid points are of a material, such as gold, that scatters the electrons into a detector. The incidence of the beam on a grid point is indicated by a jump in the signal from the detector.
Since the positions of the points of the calibration plate are known, the knowledge of these positions is used to correct the measured values of the positions. This correction is achieved by a calibration function which maps the measured values into calibrated- measured values. By definition, the calibration mapping is such that the calibrated measured values equal the known values of the positions of the grid points. In one approach, a two dimensional calibration polynomial is utilized to convert the uncalibrated measurements to calibrated measurements. The calibration process then involves the determination of the coefficients in the calibration polynomial so that the calibrated measurements of the points in the calibration grid equal the known positions of the points in the grid. In some versions of this approach, the form of the calibration polynomial is determined by assumptions about the sources of the measurement errors. For example, the interferometer mirrors can be modelled as having a small second order correction to being optically flat. Also, terms can be included to account for small rotations (i.e., roll, pitch and yaw) of the wafer stage as it is translated. Unfortunately, the positional accuracy required for current state of the art processes such as electron beam lithography is such that the supposed locations of the points in a calibration grid can have as much error as the positional measurement system to be calibrated. Therefore, the positions of the grid points can no longer be treated as known values to which the measured values can be adjusted. Thus, what is required is a calibration process in which calibration is achieved using a calibration plate in which the positions of the grid points are not precisely known.
In one approach, a calibration plate having grid points at imprecisely known locations is placed on the wafer stage and the locations of the grid points are measured. The grid plate is then rotated by 90 degrees about its center two or more times and in each of these orientations the positions of the grid points are measured. A finite calibration polynomial is assumed and the number of measurements is greater than the number of unknowns so that this information is utilized to find the unknown coefficients of the calibration polynomial. As is shown below in the Summary of the invention, there is some surprising indeterminacy in this approach so that it leads to an incomplete calibration of the system.